Eulerian collinear configuration for 3-body problem

2019/10/01 by Liang Ding, Ding, Liang, Juan Manuel Sánchez-Cerritos +3
Mathematics · Engineering · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Spacecraft Dynamics and Control #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1910.00367

Abstract

For 3-body problem with any given masses m₁, m₂, m₃>0, there exist only Eulerian collinear central configuration and Lagrangian equilateral-triangle central configuration, and in this paper, for planar 3-body problem, we prove that there exists another non-collision trajectory q, which is not the variational minimizer of the Lagrangian action on the loop space Λ₁, is also an Eulerian collinear central configuration at any instant. Moreover, we do not need the restriction condition on the winding number deg(q_i-q_j)≠0 (i≠ j).

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